The most secure way to destroy bitcoins is to send them to a script that can never return true, and which includes the reference code that confirms the goal of destroying these coins. I don't know of readily available software tools that can do that, and I'm not sure the network will accept these transactions.
Here's a simple method everyone can try at home:...
You can do this manually using the hex/base58check converter (such as the converter on brainwallet.org)
Remove the starting 1 and convert from base58 XXXXXXXXXXXXXXXXXXXXXXXXXXX to hex: 25c7415deb828c49ccb799c452ae17589bca1af2 (make sure result is 24 bytes)
Remove last 4 bytes to get a 20-byte hash:
25c7415deb828c49ccb799c452ae17589bca1af2 -> ...
There is no way to determine (that I can imagine) the number of lost private keys, you would have to make a guess that after x years without movement the private key is lost but that would just be a guess.
If you want to use an address, it would be nice to generate an address that can be verified by a human as obviously unspendable just by looking at the Base58. When you look at these addresses, you will say, "wow, that is obviously unspendable."
1CounterpartyXXXXXXXXXXXXXXXUWLpVr <- used by Counterparty
1ChancecoinXXXXXXXXXXXXXXXXXZELUFD <- used by ...
what is 111...1114oLvT2?
See also here, it explains in detail on the logic behind „proof of burn“, including op_return.
why 14,270 BTC?
We cannot know. Pure speculation would be, that people write scripts, to do a proof of burn. Or also, they could provide a P2SH tx, where the hash of a text is provided. Think of it as „I can proof, that I had ...
since the government controls the physical internet
They do not (at least in North America or Europe). The internet is a network of communication. An Internet Service Provider (ISP) can be private or public, but either way it's function is to direct addressed transmissions to those addresses (IP addresses).
This network is a kind of base layer. The early ...
A digital currency with user-defined anonymity will cause any estimates to simply be guesstimates.
There are other areas where studies have attempted to quantify something and simply have concluded there is no reliable way to come up with the number so rather than provide misinformation there simply is no estimate made.
Essentially you could give a ...
The methods described by DeathAndTaxes are appropriate. The OP_RETURN method is clearly the best if you want to adhere to the bitcoin recommendations.
However, I would like to present an alternative method where you can provably burn coins and also include sufficient information in the address. We used this method in the first versions of OpenBazaar and it ...
If you just want to make it clear that you no longer own them you can just send yourself 1 santoshi and put the rest up as a fee. If you want to destroy them there are a couple decent address to send them to in What is the Bitcoin equivalent of /dev/null?
EDIT: there are better answers here: How to generate a valid bitcoin address for destroying bitcoins?
Bitcoins can be divided up infinitely. So if there was just one bitcoin left (the rest are lost) then there can still be a viable economy with fractions of bitoins.
Lost wallets are only a problem for the people who lost them, not for bitcoin. It would of course limit supply and push the the cost of bitcoins versus other currencies.